Theorem rblem2 1523

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
rblem2	|- (-. (ch \/ ph) \/ (ch \/ (ph \/ ps)))

Proof of Theorem rblem2

Step	Hyp	Ref	Expression
1		rb-ax2 1518	. . 3 |- (-. (ps \/ ph) \/ (ph \/ ps))
2		rb-ax3 1519	. . 3 |- (-. ph \/ (ps \/ ph))
3	1, 2	rbsyl 1521	. 2 |- (-. ph \/ (ph \/ ps))
4		rb-ax1 1517	. 2 |- (-. (-. ph \/ (ph \/ ps)) \/ (-. (ch \/ ph) \/ (ch \/ (ph \/ ps))))
5	3, 4	anmp 1516	1 |- (-. (ch \/ ph) \/ (ch \/ (ph \/ ps)))

Syntax hints:  -. wn 3   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by:  rblem3  1524  rblem4  1525  re2luk3  1532